I had the LL2.1 Deluxe in-house for a few months and rolled through several different NOS 6DJ8 family members. I concluded from the impressive results of doing so that, were I to be an LL2 owner, such a swap out would be mandatory. I had no 12AU7s on hand to try but speculate similar result. If you're familiar with the house sound of 6DJ8/6922/7308 brands you know what they do, and likewise that choosing one over the other is a matter of personal taste. Amperex Orange Globes,and Valvos worked very well. Best to my ears were Siemens 7308s (late '60's if I recall) which yielded distinctly improved image specificity and upper octave extension.
Wrt dampers I don't know that their use would be any more or less preamp specific than with any other unit. Herbies' dampers work well.
The Lamm's built in AC filters may mitigate the effect of some power cords. My suggestion is first to learn its character with the stock cord and then experiment. I used a Shunyata Python coming from a Shunyata V-Ray with positive results.
Feed your most used source to the Direct input. I heard it as ever so slightly clearer compared with the Line input.
Congrats on the upgrade - the LL2.1 is a real sweetheart.